Gábor Braun
Georgia Institute of Technology
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Publication
Featured researches published by Gábor Braun.
Mathematics of Operations Research | 2015
Gábor Braun; Samuel Fiorini; Sebastian Pokutta; David Steurer
We develop a framework for proving approximation limits of polynomial size linear programs (LPs) from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any LP as opposed to only programs generated by hierarchies. Using our framework, we prove that O(n1/2-ϵ)-approximations for CLIQUE require LPs of size 2nΩ(ϵ). This lower bound applies to LPs using a certain encoding of CLIQUE as a linear optimization problem. Moreover, we establish a similar result for approximations of semidefinite programs by LPs. Our main technical ingredient is a quantitative improvement of Razborov’s [38] rectangle corruption lemma for the high error regime, which gives strong lower bounds on the nonnegative rank of shifts of the unique disjointness matrix.
symposium on discrete algorithms | 2015
Gábor Braun; Sebastian Pokutta
The groundbreaking work of Rothvo{\ss} [arxiv:1311.2369] established that every linear program expressing the matching polytope has an exponential number of inequalities (formally, the matching polytope has exponential extension complexity). We generalize this result by deriving strong bounds on the polyhedral inapproximability of the matching polytope: for fixed
Crelle's Journal | 2010
Gábor Braun; András Némethi
0 < \varepsilon < 1
Compositio Mathematica | 2007
Gábor Braun; András Némethi
, every polyhedral
Computational Complexity | 2017
Gábor Braun; Rahul Jain; Troy Lee; Sebastian Pokutta
(1 + \varepsilon / n)
symposium on discrete algorithms | 2016
Gábor Braun; Jonah Brown-Cohen; Arefin Huq; Sebastian Pokutta; Prasad Raghavendra; Aurko Roy; Benjamin Weitz; Daniel Zink
-approximation requires an exponential number of inequalities, where
SIAM Journal on Discrete Mathematics | 2016
Gábor Braun; Sebastian Pokutta
n
IEEE Transactions on Information Theory | 2015
Gábor Braun; Sebastian Pokutta
is the number of vertices. This is sharp given the well-known
integer programming and combinatorial optimization | 2016
Gábor Braun; Sebastian Pokutta; Aurko Roy
\rho
allerton conference on communication, control, and computing | 2014
Gábor Braun; Sebastian Pokutta; Yao Xie
-approximation of size